%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : RNG062+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:25:45 AM UTC 2026
% Result : Theorem 40.38s 6.42s
% Output : CNFRefutation 40.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 41 ( 13 unt; 0 def)
% Number of atoms : 121 ( 24 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 160 ( 80 ~; 65 |; 11 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 35 ( 13 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mSZeroSc,axiom,
aScalar0(sz0z00) ).
fof(mSumSc,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtpldt0(X0,X1)) ) ).
fof(mMulSc,axiom,
! [X0,X1] :
( ( aScalar0(X1)
& aScalar0(X0) )
=> aScalar0(sdtasdt0(X0,X1)) ) ).
fof(mNegSc,axiom,
! [X0] :
( aScalar0(X0)
=> aScalar0(smndt0(X0)) ) ).
fof(mArith,axiom,
! [X0,X1,X2] :
( ( aScalar0(X2)
& aScalar0(X1)
& aScalar0(X0) )
=> ( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
& sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
& sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
& sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ) ) ).
fof(m__1892,hypothesis,
( xR = sdtasdt0(xC,xG)
& aScalar0(xR) ) ).
fof(m__1930,hypothesis,
( xS = sdtasdt0(xF,xD)
& aScalar0(xS) ) ).
fof(m__2144,hypothesis,
( sdtasdt0(smndt0(xS),smndt0(xS)) = sdtasdt0(xS,xS)
& sdtasdt0(smndt0(xS),xR) = smndt0(xN)
& sdtasdt0(xR,smndt0(xS)) = smndt0(xN) ) ).
fof(m__2221,hypothesis,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) ).
fof(m__,conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)) ).
fof(negated_conjecture,negated_conjecture,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(negate_conjecture,[status(cth)],[m__]) ).
cnf(c7,plain,
aScalar0(sz0z00),
inference(clausification,[status(esa)],[mSZeroSc]) ).
cnf(c8,plain,
( aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mSumSc]) ).
cnf(c9,plain,
( aScalar0(sdtasdt0(X0,X1))
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mMulSc]) ).
cnf(c10,plain,
( aScalar0(smndt0(X0))
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mNegSc]) ).
cnf(c20,plain,
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mArith]) ).
cnf(c21,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aScalar0(X2)
| ~ aScalar0(X1)
| ~ aScalar0(X0) ),
inference(clausification,[status(esa)],[mArith]) ).
cnf(c83,plain,
aScalar0(xR),
inference(clausification,[status(esa)],[m__1892]) ).
cnf(c87,plain,
aScalar0(xS),
inference(clausification,[status(esa)],[m__1930]) ).
cnf(c94,plain,
sdtasdt0(smndt0(xS),xR) = smndt0(xN),
inference(clausification,[status(esa)],[m__2144]) ).
cnf(c97,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) = sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),
inference(clausification,[status(esa)],[m__2221]) ).
cnf(c98,plain,
sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtasdt0(xS,xS)),smndt0(xN)),smndt0(xN)),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtasdt0(xS,xS))
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))),smndt0(xN)) ),
inference(superposition,[status(thm)],[c20,c98]) ).
cnf(d1,plain,
( ~ aScalar0(X0)
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),smndt0(xN)) ),
inference(superposition,[status(thm)],[c21,d0]) ).
cnf(d2,plain,
( ~ aScalar0(xR)
| ~ aScalar0(smndt0(xS))
| aScalar0(smndt0(xN)) ),
inference(superposition,[status(thm)],[c94,c9]) ).
cnf(d3,plain,
( aScalar0(smndt0(xN))
| ~ aScalar0(smndt0(xS)) ),
inference(resolution,[status(thm)],[c83,d2]) ).
cnf(d4,plain,
( ~ aScalar0(xS)
| aScalar0(smndt0(xN)) ),
inference(resolution,[status(thm)],[d3,c10]) ).
cnf(d5,plain,
aScalar0(smndt0(xN)),
inference(resolution,[status(thm)],[c87,d4]) ).
cnf(d6,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),sdtpldt0(smndt0(xN),sdtasdt0(xS,xS))),smndt0(xN)) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( ~ aScalar0(X2)
| ~ aScalar0(X0)
| ~ aScalar0(X1)
| ~ aScalar0(X3)
| ~ aScalar0(sdtpldt0(X0,X1))
| ~ aScalar0(X2)
| sdtpldt0(sdtpldt0(X0,sdtpldt0(X1,X2)),X3) = sdtpldt0(sdtpldt0(X0,X1),sdtpldt0(X2,X3)) ),
inference(superposition,[status(thm)],[c20,c20]) ).
cnf(d8,plain,
( ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtpldt0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)),sdtpldt0(sdtasdt0(xS,xS),smndt0(xN))) ),
inference(superposition,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)))
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(demodulation,[status(thm)],[d8,c97]) ).
cnf(d10,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)))
| ~ aScalar0(X0)
| sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) != sdtasdt0(sdtpldt0(xR,smndt0(xS)),sdtpldt0(xR,smndt0(xS))) ),
inference(resolution,[status(thm)],[d5,d9]) ).
cnf(d11,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(sdtpldt0(sdtasdt0(xR,xR),smndt0(xN)))
| ~ aScalar0(X0) ),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(smndt0(xN))
| ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[d11,c8]) ).
cnf(d13,plain,
( ~ aScalar0(sdtasdt0(xS,xS))
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[d5,d12]) ).
cnf(d14,plain,
( ~ aScalar0(xS)
| ~ aScalar0(xS)
| ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[d13,c9]) ).
cnf(d15,plain,
( ~ aScalar0(sdtasdt0(xR,xR))
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[c87,d14]) ).
cnf(d16,plain,
( ~ aScalar0(xR)
| ~ aScalar0(xR)
| ~ aScalar0(X0) ),
inference(resolution,[status(thm)],[d15,c9]) ).
cnf(d17,plain,
~ aScalar0(X0),
inference(resolution,[status(thm)],[c83,d16]) ).
cnf(d18,plain,
$false,
inference(resolution,[status(thm)],[d17,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : RNG062+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.36 % Computer : n020.cluster.edu
% 0.07/0.36 % Model : x86_64 x86_64
% 0.07/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.36 % Memory : 8046.5625MB
% 0.07/0.36 % OS : Linux 6.8.0-71-generic
% 0.07/0.36 % CPULimit : 300
% 0.07/0.36 % WCLimit : 300
% 0.07/0.36 % DateTime : Sat Sep 26 05:56:34 UTC 2026
% 0.07/0.37 % CPUTime :
% 0.07/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.38/6.42 % SZS status Theorem for theBenchmark.p
% 40.38/6.42 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------